Calculus volume stuff

posted by Roni

Find the volume of the solid obtained by rotating the region bounded
y = 16 x and y = 2 x^2 about y =0

Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0

Find the volume of the solid generated by rotating the region bounded by
y = \sin^2(x) and y = 0
between 0 and pi about the x-axis

  1. Steve

    washers: v=∫[0,8] π(R^2-r^2) dx
    where R=16x and r=2x^2
    = 2621454/15 π

    shells: v=∫[0,128] 2πrh dy
    where r=y and h=√(y/2)-y/16
    = 2621454/15 π

    Can you set up the other integrals?

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